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Journal of Alloys and Compounds 645 (2015) 283–289
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Reversible and irreversible DC magnetization processes in the frame of magnetic, thermal and electrical properties of Fe-based composite materials Zuzana Bircˇáková a,⇑, Peter Kollár a, Bernd Weidenfeller b, Ján Füzer a, Mária Fáberová c, Radovan Bureš c a b c
Institute of Physics, Faculty of Science, Pavol Jozef Šafárik University, Park Angelinum 9, 04154 Košice, Slovakia Institute of Electrochemistry, Technical University of Clausthal, Arnold-Sommerfeld-Str. 6, 38678 Clausthal-Zellerfeld, Germany Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 04353 Košice, Slovakia
a r t i c l e
i n f o
Article history: Received 16 April 2015 Received in revised form 13 May 2015 Accepted 14 May 2015 Available online 19 May 2015 Keywords: Composite materials Magnetic measurements Powder metallurgy Thermodynamic properties Reversible permeability Energy losses
a b s t r a c t Proportions of reversible and irreversible magnetization processes in the overall magnetization process were studied in a complex view of magnetic, thermal and electrical properties of iron–phenolphormaldehyde resin composites. They were determined experimentally at different values of magnetic induction along the initial curve. The results of total, differential, reversible and irreversible permeability measurement as well as the analysis of DC energy losses revealed the same tendencies: The numbers of movable domain walls (determining the extent of reversible processes) depend on the magnetic particle size and the resin content through the demagnetizing fields produced by the particle surfaces, lowering the interaction between particles. Thermal diffusivity was compared with Hashin–Shtrikman model indicating good insulation of particles. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Soft magnetic composites (SMCs) are a remarkable kind of soft magnetic materials composed of small ferromagnetic particles insulated from each other. They possess certain very good electromagnetic and mechanical properties e.g. the magnetic and thermal isotropy, extremely low classical losses and relatively low total energy losses at medium and higher frequencies (due to an insulating layer between iron powder particles the eddy currents are minimized), as well as a nearly netshape fabrication process ensuring a low cost mass production, which all makes them able to compete with traditionally used materials such as FeSi steels or soft magnetic ferrites at a similar production cost or even cheaper [1–5]. SMCs are well suited for use in alternating magnetic fields for electromagnetic applications such as cores with three dimensional ferromagnetic behaviour for transformers and electromotors, also as the electromagnetic circuits, sensors, electromagnetic actuation devices, low frequency filters, induction field coils, magnetic seal systems and magnetic field shielding [3–7]. One of the advantages of SMCs are their relatively low energy losses at medium and higher frequencies compared to FeSi steels – the cross-over point ⇑ Corresponding author. Tel.: +421 908 525 843. E-mail address: [email protected] (Z. Bircˇáková). http://dx.doi.org/10.1016/j.jallcom.2015.05.121 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.
is about 400 Hz, where the losses for both materials are similar (at 1.5 T of about 90 W/kg, according to [1]). SMCs are typically produced by the powder metallurgy processing methods – depending on the chosen combinations of materials and processing parameters, a wide range of properties can be obtained, so the electromagnetic and mechanical properties of SMCs can be tuned, within their physical limits, to the requirements of particular application [3–6]. The investigation of reversible and irreversible magnetization processes can provide valuable information on behaviour of magnetic materials at different magnetic flux densities or magnetizing frequencies and also finding the parameters influencing their proportions in the overall magnetization process can be of advantage enabling to produce materials with the required properties. Particularly studying the processes at DC magnetization is the starting point important also for the analysis of AC magnetization process. Up to now several works have dealt with the reversible and irreversible magnetization processes in various materials [8– 11], but they have not yet been studied in SMCs by means of the reversible permeability measurement. It is also important to study the thermal and electrical properties of magnetic materials as an energy dissipation occurs due to magnetization processes and the magnetic components of electromagnetic devices are heated through the Joule effect of eddy
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currents induced by time dependent changes of magnetic induction in material [12,13]. The aim of this work was to find: – the proportions of reversible and irreversible magnetization processes according to the differential, reversible and irreversible relative permeability measurements, – the relation between reversible and irreversible magnetization processes and magnetic, thermal and electrical properties as a function of magnetic induction, temperature, the mean magnetic particle size and the resin content of iron–phenolphormaldehyde resin composites. 2. Experimental details Ring composite samples were prepared by powder metallurgy (outer diameter 24 mm, inner diameter 18 mm, height from 1.4 to 2.4 mm) for magnetic and electrical properties investigations, and thin discs (diameter 10 mm, height from 1.5 to 2.2 mm) were used for thermal properties measurements. To study the SMC properties as a function of mean magnetic particle size and resin content, the polycrystalline iron powder ASC 100.29 (Höganäs AB Sweden [14]) was sieved obtaining four granulometric classes of particle size distributions with peaks at 45 lm, 75 lm, 100 lm and 160 lm (classes labelled F45, F75, F100 and F160). For each granulometric class samples with different iron to resin ratios were prepared. Iron powder was homogenized with 5 vol.%, 10 vol.% and 15 vol.% (1 wt.%, 2 wt.% and 3 wt.%) of phenolphormaldehyde resin (Bakelite ATM) and acetone, then compacted at uniaxial pressure of 800 MPa and afterwards cured at a temperature of 165 °C for 60 min in electric furnace in air. Density and porosity were calculated from the mass and dimensions of prepared samples (density of iron: 7.851 g/cm3, density of resin: 1.39 g/cm3), reaching values about 6.7 g/cm3 (samples with 5 vol.% of resin), 6.0 g/cm3 (10 vol.% of resin) and 5.6 g/cm3 (15 vol.% of resin), porosity varied from 10% to 18%. For the investigation of magnetic properties the initial magnetization curves were measured by the DC fluxmeter-based hysteresisgraph, from which the total and the differential relative permeability were further obtained. DC energy losses were calculated from the hysteresis loops measured by DC fluxmeter-based hysteresisgraph. Maximum induction was measured referred to the filler content of ferromagnetic material in composite sample (subtracting non-ferromagnetic components: resin and pores). The reversible relative permeability vs. magnetic field dependences were measured using the setup shown in Fig. 1. The following method was used: starting from the demagnetized state the DC magnetic field is set first, then the small AC magnetic field is applied and the induced voltage is read by the lock-in amplifier (a similar setup was used for steel sheets measurement in [11]). For the AC field amplitude approaching zero the additional small inner hysteresis loop becomes a line and the slope determines the reversible permeability.
To measure only reversible magnetization the frequency and the amplitude of AC magnetic field must be very low. The condition was fulfilled with the used values ranging from 30 Hz to 90 Hz and from 5 A/m to 8 A/m, respectively, depending on the sample resin content. For the investigation of thermal properties the thermal diffusivity was measured by the laser flash apparatus (LFA 427, Netzsch-Gerätebau GmbH, Germany) in the temperature range from 40 to 200 °C. Cylinder-shaped samples were covered by a thin graphite layer for a good absorption of the laser beam [15]. The specific resistivity was measured by the four-contact method adapted for ring-shaped samples.
3. Magnetic properties – reversible permeability, DC energy losses and the proportions of magnetization processes One of the key quantities characterizing the magnetic properties of magnetic materials is the magnetic permeability. In relation to the initial magnetization curve it is defined by various means. The total relative permeability ltot is calculated as
ltot ¼
B
ð1Þ
;
l0 H
wherein B is the magnetic induction, H is the applied magnetic field and l0 is the magnetic constant. The differential relative permeability ldiff comprises both reversible and irreversible magnetization processes and can be written as a sum of the reversible and irreversible relative permeability, ldiff = lrev + lirr. The derivative of initial magnetization curve (denote each its point [H0, B0]) determines
ldiff
ldiff ¼
1
l0
dB dH
ð2Þ
: H0 ;B0
The reversible relative permeability lrev is defined as follows: at the point of initial magnetization curve with the DC field H1 ([H1, B1]) a small AC magnetic field of an amplitude DH/2 is applied. For DH ? 0 the additional inner hysteresis loop becomes a line. The slope of this line, where only reversible processes are present, is of smaller angle than the slope of the initial curve at the same point. It characterizes lrev as follows:
lrev ¼
1
lim
l0 DH!0
DB DH
: H1 ;B1
Fig. 1. Schematic arrangement of the equipment for reversible permeability measurement.
ð3Þ
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lrev determines the percent proportion krev of the reversible magnetization processes in the overall magnetization process at each point of the initial curve, krev ¼ ðlrev =ldiff Þ100%:
ð4Þ
The irreversible relative permeability lirr is consequently taken to be the difference between the differential and the reversible relative permeability:
lirr ¼ ldiff lrev :
ð5Þ
The relative permeabilities as the functions of B or H have its characteristic dependences for each ferromagnetic material. In Fig. 2 the total, differential, reversible and irreversible relative permeability of the sample F45 – 10% as a function of magnetic field are depicted. Qualitatively the dependences in case of magnetic composite materials show the same behaviour as the majority of ferromagnetic materials [1,12]: ldiff rises with magnetic field more steeply than ltot, having its maximum at the inflection point of initial magnetization curve (at lower field value than ltot), then the decrease of ldiff is also steeper. lrev slightly decreases with the field, starting from the initial value (together with ldiff and ltot) and ending at the value one with H ? 1, as ldiff and ltot do. lirr starts from zero at H ? 0 showing maximum also at the initial curve inflection point and ends at zero with H ? 1. In order to enable a comparison of permeability values between the samples, their dependences are further plotted as a function of magnetic induction instead of the measured dependences vs. magnetic field (assigned using initial magnetization curves). This is necessary because different magnetic field strengths are needed to reach the same value of the induction in ferromagnetic component of composite sample differing in magnetic particle size and resin content, depending on the demagnetizing fields produced by magnetic particle surfaces [13,16]. The differential and the reversible permeability as a function of magnetic induction are plotted for samples of the same granulometric class F45 with different resin content, Fig. 3(a), and for samples with the same resin content 10 vol.% for the granulometric classes F45, F75, F100 and F160, Fig. 3(b). It can be seen that the permeability values are decreasing with increasing resin content and decreasing particle size, which is caused by demagnetizing fields of particles and was also observed in [13,16,17]: The lower is the content of
Fig. 2. Total, differential, reversible and irreversible relative permeability of the sample F45 – 10% (10% defines the volume content of the resin) as a function of magnetic field. For H ? 0 A/m it is ltot = ldiff = lrev = li, where li is the initial permeability.
Fig. 3. Experimental dependences of differential and reversible relative permeability as a function of magnetic induction plotted for samples of the class F45 with different resin content – 5, 10 and 15 vol.% (a) and for samples with the resin content 10 vol.% for the classes F45, F75, F100 and F160 (b).
ferromagnetic material the higher amount of gaps between the particles causes a cut-off of magnetic flux and the higher demagnetizing fields arise (produced by magnetic poles at particle surfaces). For the case of larger particle size the number of particles in sample is reduced at a constant amount of ferromagnetic material, standing for less particle surfaces and lower demagnetizing fields produced by surface magnetic poles. From the values of ldiff and lrev the proportions krev of reversible magnetization processes were calculated (Eq. (4)) at the points of magnetic induction 0 T, 0.1 T, 0.2 T, 0.4 T, 0.6 T and 0.8 T for all samples, Fig. 4. At very low inductions B ? 0 T (Rayleigh region) only reversible domain wall displacements are present (ldiff = lrev) and the proportions start at 100%. As magnetic field increases, first irreversible domain wall displacement (Barkhausen jump) appears. The magnetization process is then realized either by Barkhausen jumps when domain walls overcome pinning energy barriers or by the reversible domain wall motion near local energy minimum between two jumps, so the amounts of reversible and irreversible domain wall displacements are comparable (assuming a statistically constant density of pinning centres). It is confirmed by the experiment: at 0.1 and 0.2 T there are about 50–65% of reversible processes (Fig. 4). At higher inductions, above Blmax, where the total permeability reaches its maximum lmax, domain wall annihilation and recreation appears [18–20]. In Table 1 Blmax determined for each sample (Eq. (1)) is given. The limit Blmax is decreasing with the increasing resin content (0.38–0.22 T). As a result of the
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resin content than at lower inductions below Blmax (cf. Table 1). In case of samples with higher resin content the rotation of magnetization vector starts playing a role at lower induction B compared to samples with lower resin content, in which magnetization process occurs by domain wall movement. In samples with higher resin content the number of movable domain walls participating in the magnetization process is lower than in samples with lower resin content due to higher demagnetizing fields produced at magnetic particles surfaces [13,16,17] reducing interaction between particles. Further at 0.6 T there are about 55–75% and at 0.8 T about 60–80% of reversible processes (Fig. 4) indicating the increasing amount of magnetization vector rotation in the magnetization process. Furthermore, for all inductions B we observe decreasing proportions of reversible processes with increasing magnetic particle size and with decreasing resin content (Fig. 4). Also this behaviour is caused by demagnetizing fields of particles resulting in a low number of movable domain walls in case of small particle sizes and higher resin content, because the pinning centres are overcome more likely in case of larger particles and lower resin content (meaning more Barkhausen jumps and therefore higher proportions of irreversible magnetization processes) due to a higher number of movable domain walls, as well as better surface to volume ratio of larger particles. The DC energy losses WDC measured at a maximum induction Bm from 0.1 to 1.0 T in ferromagnetic material were divided into high low induction loss W low DC and high induction loss W DC components [18–20], Fig. 5. The low and high induction losses were plotted vs. maximum induction Bm which can be seen in Fig. 6. Low induction losses come from the energy dissipation due to domain wall displacements and high induction losses are related to magnetization vector rotation as well as domain wall annihilation and recreation
Fig. 4. Proportions of reversible magnetization processes at magnetic induction 0 T, 0.1 T, 0.2 T, 0.4 T, 0.6 T and 0.8 T for the investigated samples.
different Blmax values in Fig. 4 proportions of reversible processes vary with the resin content. The proportions of reversible processes at 0.4 T are with 70% slightly higher especially for 10% and 15%
[18–20]. The cross-over point, where W high exceed W low DC , is less DC than 0.6 T, 0.7 T and 0.9 T for samples with 15 vol.%, 10 vol.% and 5 vol.% of resin, respectively (Fig. 6). The tendencies are in agreement with the proportions in Fig. 4. It can be seen that the high induction losses of samples with 5% resin content are clearly lower than for samples with 10% or 15% resin content. Contrary, with increasing resin content the low induction losses are increased. This behaviour indicates the higher probability of magnetization vector rotation, domain wall annihilation and recreation and also the lower probability of irreversible domain wall displacements with increasing resin content. The DC energy losses WDC of samples with 10 vol.% of resin measured at maximum induction Bm from 0.1 to 1.0 T (in ferromagnetic component of SMC) are shown in Fig. 7 for samples only differing in magnetic particle sizes while technological manufacturing process, resin content and used materials were identical. The decrease of WDC with the increasing particle size was observed for Bm starting from 0.2 T up to the maximum measured value 1.0 T (Fig. 7) which can be related to the predominance of Barkhausen jumps in this range of induction Bm. Furthermore, in case of smaller particle sizes the higher amount of particles stands also for more pinning sites hindering the domain wall movement (defects as well as particle surfaces) [13,21,22]. Values of WDC for Bm of 0.1 T show even a slight increase with the increasing particle sizes – Fig. 7. At very low inductions Bm the reversible domain wall displacements play a dominant role and we assume that in this case, conversely, the higher number of particles in sample is of advantage, as more movable domain walls can be present than in the composite with larger particles but a lower number of particles.
Table 1 Magnetic induction Blmax where total permeability reaches maximum (values for each resin content are approximately identical within the measurement error of 0.01 T). Sample
F45-5%
F75-5%
F100-5%
F160-5%
F45-10%
F75-10%
F100-10%
F160-10%
F45-15%
F75-15%
F100-15%
F160-15%
Blmax (T)
0.37
0.37
0.38
0.37
0.27
0.28
0.27
0.28
0.23
0.22
0.23
0.23
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Fig. 5. Determination of low and high induction losses on hysteresis loop.
4. Thermal and electrical properties Since the magnetic components in electromagnetic devices are usually being heated during their operation in AC magnetic fields, it is considered to be of importance to investigate also the thermal properties of magnetic materials, particularly the heat outflow to prevent the component overheating. It is especially needed when a composite material cannot be operated under higher temperatures e.g. when it contains an organic binder. One of the key quantities characterizing thermal behaviour of materials is the thermal diffusivity a, which describes the heat flowing rate through a material – the ability to conduct the thermal energy relative to the ability to store it [23,24]. A few models exist for thermal diffusivity of heterogeneous materials, e.g. the Parallel model, the Agari-Uno model, the symmetric and asymmetric Bruggeman model or the Cheng-Vachon model [15,24], some of them not originally developed for the thermal diffusivity calculation, but applying mathematical analogy to various transport coefficients. One of such mathematical models holding for e.g. electric conductivity, heat conductivity, thermal diffusivity, electric permittivity or magnetic permeability of a composite material is the model by Hashin and Shtrikman [15,25], originally developed for magnetic permeability of a homogeneous multi-phase system. In general the thermal diffusivity a of a homogeneous body is defined as the thermal conductivity k divided by the density q and the specific heat capacity cP at a constant pressure [23,24] (unit mm2 s1):
a¼
k
qc P
ð6Þ
:
According to the Hashin and Shtrikman model the thermal diffusivity a of SMC composed of a resin matrix with thermal diffusivity aR and a volume fraction of iron particles x with thermal diffusivity aFe is calculated first as the case when iron particles are perfectly insulated by the resin, this is represented by the Hashin–Shtrikman lower boundary HS
a ¼ aHS ¼ aR
2aR þ aFe 2xðaR aFe Þ : 2aR þ aFe þ xðaR aFe Þ
ð7Þ
As the opposite theoretical case one can assume the iron particles are no longer insulated and the iron becomes the matrix surrounding the resin parts. Then a equals to the Hashin–Shtrikman upper boundary HS+
a ¼ aHSþ ¼ aFe
2aFe þ aR 2ð1 xÞðaFe aR Þ : 2aFe þ aR þ ð1 xÞðaFe aR Þ
ð8Þ Fig. 6. High and low induction losses vs. maximum magnetic induction.
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Fig. 7. DC energy losses of samples with 10 vol.% of resin at Bm from 0.1 T to 1.0 T (in ferromagnetic material).
Real SMC can be usually found between HS and HS+, depending on the quality of insulation of magnetic particles from each other. Schilling and Partzsch [26] calculated the interconnectivity Xic from aHS, aHS+ and experimental value aexp, determining the extent to which iron particles form an ideally interconnected network. The closer the measured value aexp is to the theoretical case of insulated particles aHS, the lower is the value of Xic (for perfectly insulated particles Xic ? 0) [15,24]:
aexp aHS X ic ¼ HSþ : a aHS
Fig. 8. Thermal diffusivity as a function of temperature.
ð9Þ
In Fig. 8 the measured dependence of thermal diffusivity on temperature in the range from 40 to 200 °C is shown, a decreases with the increasing resin content, as expected, but no dependence on magnetic particle size was observed (also found in [15]). The decrease of a with temperature is due to the increase of the velocity v and free path length l of phonons, a = 1/(3vl). From Eqs. (7), (8) lower and upper boundary HS and HS+ were calculated (aFe 23 mm2 s1, aR 0.1 mm2 s1 – literature values for t 25 °C [27], and the porosity was taken into account with a of an air at high compacting pressure to be even lower than aR [28]), in Table 2 values of aHS and aHS+ are shown for samples with 5 vol.%, 10 vol.% and 15 vol.% of resin. We see that the measured values of a for all samples are much closer to lower boundary HS than to upper boundary HS+, revealing that iron particles are relatively well insulated from each other. This fact is also confirmed by low values of Xic (calculated from Eq. (9)). In Table 2 the ranges of minimum to maximum values for each volume fraction of the resin are shown. In the view of practical application of soft magnetic composite material, in which thanks to the particle insulation much lower values of energy losses can be reached causing lower heating of the composite, the much lower thermal diffusivity compared to bulk iron material is then sufficient for the lower heat outflow rate. The measured specific electrical resistivity qR as a function of mean magnetic particle size is plotted in Fig. 9. It was observed that qR decreases with the increasing magnetic particle size: for samples with 15 vol.% of resin it was from 360 mX m down to 1.4 mX m, for samples with 10 vol.% of resin from 16 mX m down to 0.8 mX m and for samples with 5 vol.% of resin from 2.2 mX m down to 0.18 mX m. Values of qR of all samples are relative high compared to similar composites investigated e.g. in [29–31], revealing good insulation of particles. Both the thermal diffusivity and the specific resistivity measurements indicate that the iron particles in composite samples
Table 2 Hashin–Shtrikman lower and upper boundaries and the interconnectivity of the samples. Samples (resin content) (vol.%)
Hashin–Shtrikman lower boundary HS (mm2 s1)
Hashin–Shtrikman upper boundary HS+ (mm2 s1)
Interconnectivity (–) (min.–max. value)
5 10 15
1.56 0.96 0.77
17.92 15.38 14.05
0.002–0.021 0.015–0.04 0.002–0.015
Fig. 9. Specific resistivity as a function of mean magnetic particle size.
are quite well insulated. The quality of insulation of magnetic particles has a direct connection with the magnetic interaction between the particles through the inner demagnetizing fields – observed and explained in [13]: The more the magnetic particles
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are insulated from each other, the higher are the demagnetizing fields causing lower interaction between the particles and resulting in lower number of movable domain walls leading to less irreversible magnetization processes overall [13]. 5. Summary and conclusions In this work the proportions of reversible and irreversible magnetization processes in iron–phenolphormaldehyde resin composite samples differing in magnetic particle size and resin content were studied in the frame of magnetic, thermal and electrical properties. The investigation was focused on the magnetic permeability, the DC energy losses, the specific resistivity as well as the thermal diffusivity. The following results were obtained: 1. At very low inductions B ? 0 T the magnetization process is 100% reversible. Depending on resin content the induction at maximum permeability Blmax (limiting induction) varies from 0.22 T to 0.38 T. At the limiting induction Blmax the magnetization process is 50–65% reversible depending on resin content. Exceeding Blmax the rotation of magnetization vector becomes more and more important and magnetization processes are reversible up to 60–80% at B = 0.8 T. Proportion of irreversible processes is decreasing with resin content and also with reduction of magnetic particle size. This can be explained by demagnetizing fields at particle surfaces leading to a decrease of number of movable domain walls, as in case of larger particles and lower resin content the higher number of movable domain walls more likely overcome pinning centres, meaning more Barkhausen jumps. These observations were verified by permeability measurements as well as by separation of losses into low and high induction losses. 2. The thermal diffusivity was found to be decreasing with the increasing resin content, but no dependence on magnetic particle size was observed (contrary to the specific resistivity, which was decreasing with increasing particle size). The comparison with Hashin–Shtrikman model indicated a good insulation of iron particles from each other, resulting in low interaction between particles and therefore a low number of movable domain walls overall.
Acknowledgements This work was realized within the frame of the projects ‘‘Centre of excellence of progressive materials with nano and submicrostructure’’ ITMS 26220120019 and ‘‘Research centre of progressive materials and technologies for present and future applications’’ ITMS 26220220186 PROMATECH, supported by the Operational Program ‘‘Research and Development’’ financed through European Regional Development Fund. This work was also supported by the Slovak Research and Development Agency under the Contract No. APVV-0222-10 MAGCOMP and by the Scientific Grant Agency of the Ministry of Education of Slovak Republic and the Slovak Academy of Sciences, project VEGA No. 1/0861/12. References [1] K.H.J. Buschow, Concise Encyclopedia of Magnetic and Superconducting Materials, Elsevier, Oxford, UK, 2005. [2] S. Giménez, T. Lauwagie, G. Roebben, W. Heylen, O. Van der Biest, Effects of microstructural heterogeneity on the mechanical properties of pressed soft magnetic composite bodies, J. Alloys Comp. 419 (2006) 299–305.
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Reversible and irreversible DC magnetization processes in the frame of magnetic, thermal and electrical properties of Fe-based composite materials Zuzana Bircˇáková a,⇑, Peter Kollár a, Bernd Weidenfeller b, Ján Füzer a, Mária Fáberová c, Radovan Bureš c a b c
Institute of Physics, Faculty of Science, Pavol Jozef Šafárik University, Park Angelinum 9, 04154 Košice, Slovakia Institute of Electrochemistry, Technical University of Clausthal, Arnold-Sommerfeld-Str. 6, 38678 Clausthal-Zellerfeld, Germany Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 04353 Košice, Slovakia
a r t i c l e
i n f o
Article history: Received 16 April 2015 Received in revised form 13 May 2015 Accepted 14 May 2015 Available online 19 May 2015 Keywords: Composite materials Magnetic measurements Powder metallurgy Thermodynamic properties Reversible permeability Energy losses
a b s t r a c t Proportions of reversible and irreversible magnetization processes in the overall magnetization process were studied in a complex view of magnetic, thermal and electrical properties of iron–phenolphormaldehyde resin composites. They were determined experimentally at different values of magnetic induction along the initial curve. The results of total, differential, reversible and irreversible permeability measurement as well as the analysis of DC energy losses revealed the same tendencies: The numbers of movable domain walls (determining the extent of reversible processes) depend on the magnetic particle size and the resin content through the demagnetizing fields produced by the particle surfaces, lowering the interaction between particles. Thermal diffusivity was compared with Hashin–Shtrikman model indicating good insulation of particles. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Soft magnetic composites (SMCs) are a remarkable kind of soft magnetic materials composed of small ferromagnetic particles insulated from each other. They possess certain very good electromagnetic and mechanical properties e.g. the magnetic and thermal isotropy, extremely low classical losses and relatively low total energy losses at medium and higher frequencies (due to an insulating layer between iron powder particles the eddy currents are minimized), as well as a nearly netshape fabrication process ensuring a low cost mass production, which all makes them able to compete with traditionally used materials such as FeSi steels or soft magnetic ferrites at a similar production cost or even cheaper [1–5]. SMCs are well suited for use in alternating magnetic fields for electromagnetic applications such as cores with three dimensional ferromagnetic behaviour for transformers and electromotors, also as the electromagnetic circuits, sensors, electromagnetic actuation devices, low frequency filters, induction field coils, magnetic seal systems and magnetic field shielding [3–7]. One of the advantages of SMCs are their relatively low energy losses at medium and higher frequencies compared to FeSi steels – the cross-over point ⇑ Corresponding author. Tel.: +421 908 525 843. E-mail address: [email protected] (Z. Bircˇáková). http://dx.doi.org/10.1016/j.jallcom.2015.05.121 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.
is about 400 Hz, where the losses for both materials are similar (at 1.5 T of about 90 W/kg, according to [1]). SMCs are typically produced by the powder metallurgy processing methods – depending on the chosen combinations of materials and processing parameters, a wide range of properties can be obtained, so the electromagnetic and mechanical properties of SMCs can be tuned, within their physical limits, to the requirements of particular application [3–6]. The investigation of reversible and irreversible magnetization processes can provide valuable information on behaviour of magnetic materials at different magnetic flux densities or magnetizing frequencies and also finding the parameters influencing their proportions in the overall magnetization process can be of advantage enabling to produce materials with the required properties. Particularly studying the processes at DC magnetization is the starting point important also for the analysis of AC magnetization process. Up to now several works have dealt with the reversible and irreversible magnetization processes in various materials [8– 11], but they have not yet been studied in SMCs by means of the reversible permeability measurement. It is also important to study the thermal and electrical properties of magnetic materials as an energy dissipation occurs due to magnetization processes and the magnetic components of electromagnetic devices are heated through the Joule effect of eddy
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currents induced by time dependent changes of magnetic induction in material [12,13]. The aim of this work was to find: – the proportions of reversible and irreversible magnetization processes according to the differential, reversible and irreversible relative permeability measurements, – the relation between reversible and irreversible magnetization processes and magnetic, thermal and electrical properties as a function of magnetic induction, temperature, the mean magnetic particle size and the resin content of iron–phenolphormaldehyde resin composites. 2. Experimental details Ring composite samples were prepared by powder metallurgy (outer diameter 24 mm, inner diameter 18 mm, height from 1.4 to 2.4 mm) for magnetic and electrical properties investigations, and thin discs (diameter 10 mm, height from 1.5 to 2.2 mm) were used for thermal properties measurements. To study the SMC properties as a function of mean magnetic particle size and resin content, the polycrystalline iron powder ASC 100.29 (Höganäs AB Sweden [14]) was sieved obtaining four granulometric classes of particle size distributions with peaks at 45 lm, 75 lm, 100 lm and 160 lm (classes labelled F45, F75, F100 and F160). For each granulometric class samples with different iron to resin ratios were prepared. Iron powder was homogenized with 5 vol.%, 10 vol.% and 15 vol.% (1 wt.%, 2 wt.% and 3 wt.%) of phenolphormaldehyde resin (Bakelite ATM) and acetone, then compacted at uniaxial pressure of 800 MPa and afterwards cured at a temperature of 165 °C for 60 min in electric furnace in air. Density and porosity were calculated from the mass and dimensions of prepared samples (density of iron: 7.851 g/cm3, density of resin: 1.39 g/cm3), reaching values about 6.7 g/cm3 (samples with 5 vol.% of resin), 6.0 g/cm3 (10 vol.% of resin) and 5.6 g/cm3 (15 vol.% of resin), porosity varied from 10% to 18%. For the investigation of magnetic properties the initial magnetization curves were measured by the DC fluxmeter-based hysteresisgraph, from which the total and the differential relative permeability were further obtained. DC energy losses were calculated from the hysteresis loops measured by DC fluxmeter-based hysteresisgraph. Maximum induction was measured referred to the filler content of ferromagnetic material in composite sample (subtracting non-ferromagnetic components: resin and pores). The reversible relative permeability vs. magnetic field dependences were measured using the setup shown in Fig. 1. The following method was used: starting from the demagnetized state the DC magnetic field is set first, then the small AC magnetic field is applied and the induced voltage is read by the lock-in amplifier (a similar setup was used for steel sheets measurement in [11]). For the AC field amplitude approaching zero the additional small inner hysteresis loop becomes a line and the slope determines the reversible permeability.
To measure only reversible magnetization the frequency and the amplitude of AC magnetic field must be very low. The condition was fulfilled with the used values ranging from 30 Hz to 90 Hz and from 5 A/m to 8 A/m, respectively, depending on the sample resin content. For the investigation of thermal properties the thermal diffusivity was measured by the laser flash apparatus (LFA 427, Netzsch-Gerätebau GmbH, Germany) in the temperature range from 40 to 200 °C. Cylinder-shaped samples were covered by a thin graphite layer for a good absorption of the laser beam [15]. The specific resistivity was measured by the four-contact method adapted for ring-shaped samples.
3. Magnetic properties – reversible permeability, DC energy losses and the proportions of magnetization processes One of the key quantities characterizing the magnetic properties of magnetic materials is the magnetic permeability. In relation to the initial magnetization curve it is defined by various means. The total relative permeability ltot is calculated as
ltot ¼
B
ð1Þ
;
l0 H
wherein B is the magnetic induction, H is the applied magnetic field and l0 is the magnetic constant. The differential relative permeability ldiff comprises both reversible and irreversible magnetization processes and can be written as a sum of the reversible and irreversible relative permeability, ldiff = lrev + lirr. The derivative of initial magnetization curve (denote each its point [H0, B0]) determines
ldiff
ldiff ¼
1
l0
dB dH
ð2Þ
: H0 ;B0
The reversible relative permeability lrev is defined as follows: at the point of initial magnetization curve with the DC field H1 ([H1, B1]) a small AC magnetic field of an amplitude DH/2 is applied. For DH ? 0 the additional inner hysteresis loop becomes a line. The slope of this line, where only reversible processes are present, is of smaller angle than the slope of the initial curve at the same point. It characterizes lrev as follows:
lrev ¼
1
lim
l0 DH!0
DB DH
: H1 ;B1
Fig. 1. Schematic arrangement of the equipment for reversible permeability measurement.
ð3Þ
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lrev determines the percent proportion krev of the reversible magnetization processes in the overall magnetization process at each point of the initial curve, krev ¼ ðlrev =ldiff Þ100%:
ð4Þ
The irreversible relative permeability lirr is consequently taken to be the difference between the differential and the reversible relative permeability:
lirr ¼ ldiff lrev :
ð5Þ
The relative permeabilities as the functions of B or H have its characteristic dependences for each ferromagnetic material. In Fig. 2 the total, differential, reversible and irreversible relative permeability of the sample F45 – 10% as a function of magnetic field are depicted. Qualitatively the dependences in case of magnetic composite materials show the same behaviour as the majority of ferromagnetic materials [1,12]: ldiff rises with magnetic field more steeply than ltot, having its maximum at the inflection point of initial magnetization curve (at lower field value than ltot), then the decrease of ldiff is also steeper. lrev slightly decreases with the field, starting from the initial value (together with ldiff and ltot) and ending at the value one with H ? 1, as ldiff and ltot do. lirr starts from zero at H ? 0 showing maximum also at the initial curve inflection point and ends at zero with H ? 1. In order to enable a comparison of permeability values between the samples, their dependences are further plotted as a function of magnetic induction instead of the measured dependences vs. magnetic field (assigned using initial magnetization curves). This is necessary because different magnetic field strengths are needed to reach the same value of the induction in ferromagnetic component of composite sample differing in magnetic particle size and resin content, depending on the demagnetizing fields produced by magnetic particle surfaces [13,16]. The differential and the reversible permeability as a function of magnetic induction are plotted for samples of the same granulometric class F45 with different resin content, Fig. 3(a), and for samples with the same resin content 10 vol.% for the granulometric classes F45, F75, F100 and F160, Fig. 3(b). It can be seen that the permeability values are decreasing with increasing resin content and decreasing particle size, which is caused by demagnetizing fields of particles and was also observed in [13,16,17]: The lower is the content of
Fig. 2. Total, differential, reversible and irreversible relative permeability of the sample F45 – 10% (10% defines the volume content of the resin) as a function of magnetic field. For H ? 0 A/m it is ltot = ldiff = lrev = li, where li is the initial permeability.
Fig. 3. Experimental dependences of differential and reversible relative permeability as a function of magnetic induction plotted for samples of the class F45 with different resin content – 5, 10 and 15 vol.% (a) and for samples with the resin content 10 vol.% for the classes F45, F75, F100 and F160 (b).
ferromagnetic material the higher amount of gaps between the particles causes a cut-off of magnetic flux and the higher demagnetizing fields arise (produced by magnetic poles at particle surfaces). For the case of larger particle size the number of particles in sample is reduced at a constant amount of ferromagnetic material, standing for less particle surfaces and lower demagnetizing fields produced by surface magnetic poles. From the values of ldiff and lrev the proportions krev of reversible magnetization processes were calculated (Eq. (4)) at the points of magnetic induction 0 T, 0.1 T, 0.2 T, 0.4 T, 0.6 T and 0.8 T for all samples, Fig. 4. At very low inductions B ? 0 T (Rayleigh region) only reversible domain wall displacements are present (ldiff = lrev) and the proportions start at 100%. As magnetic field increases, first irreversible domain wall displacement (Barkhausen jump) appears. The magnetization process is then realized either by Barkhausen jumps when domain walls overcome pinning energy barriers or by the reversible domain wall motion near local energy minimum between two jumps, so the amounts of reversible and irreversible domain wall displacements are comparable (assuming a statistically constant density of pinning centres). It is confirmed by the experiment: at 0.1 and 0.2 T there are about 50–65% of reversible processes (Fig. 4). At higher inductions, above Blmax, where the total permeability reaches its maximum lmax, domain wall annihilation and recreation appears [18–20]. In Table 1 Blmax determined for each sample (Eq. (1)) is given. The limit Blmax is decreasing with the increasing resin content (0.38–0.22 T). As a result of the
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resin content than at lower inductions below Blmax (cf. Table 1). In case of samples with higher resin content the rotation of magnetization vector starts playing a role at lower induction B compared to samples with lower resin content, in which magnetization process occurs by domain wall movement. In samples with higher resin content the number of movable domain walls participating in the magnetization process is lower than in samples with lower resin content due to higher demagnetizing fields produced at magnetic particles surfaces [13,16,17] reducing interaction between particles. Further at 0.6 T there are about 55–75% and at 0.8 T about 60–80% of reversible processes (Fig. 4) indicating the increasing amount of magnetization vector rotation in the magnetization process. Furthermore, for all inductions B we observe decreasing proportions of reversible processes with increasing magnetic particle size and with decreasing resin content (Fig. 4). Also this behaviour is caused by demagnetizing fields of particles resulting in a low number of movable domain walls in case of small particle sizes and higher resin content, because the pinning centres are overcome more likely in case of larger particles and lower resin content (meaning more Barkhausen jumps and therefore higher proportions of irreversible magnetization processes) due to a higher number of movable domain walls, as well as better surface to volume ratio of larger particles. The DC energy losses WDC measured at a maximum induction Bm from 0.1 to 1.0 T in ferromagnetic material were divided into high low induction loss W low DC and high induction loss W DC components [18–20], Fig. 5. The low and high induction losses were plotted vs. maximum induction Bm which can be seen in Fig. 6. Low induction losses come from the energy dissipation due to domain wall displacements and high induction losses are related to magnetization vector rotation as well as domain wall annihilation and recreation
Fig. 4. Proportions of reversible magnetization processes at magnetic induction 0 T, 0.1 T, 0.2 T, 0.4 T, 0.6 T and 0.8 T for the investigated samples.
different Blmax values in Fig. 4 proportions of reversible processes vary with the resin content. The proportions of reversible processes at 0.4 T are with 70% slightly higher especially for 10% and 15%
[18–20]. The cross-over point, where W high exceed W low DC , is less DC than 0.6 T, 0.7 T and 0.9 T for samples with 15 vol.%, 10 vol.% and 5 vol.% of resin, respectively (Fig. 6). The tendencies are in agreement with the proportions in Fig. 4. It can be seen that the high induction losses of samples with 5% resin content are clearly lower than for samples with 10% or 15% resin content. Contrary, with increasing resin content the low induction losses are increased. This behaviour indicates the higher probability of magnetization vector rotation, domain wall annihilation and recreation and also the lower probability of irreversible domain wall displacements with increasing resin content. The DC energy losses WDC of samples with 10 vol.% of resin measured at maximum induction Bm from 0.1 to 1.0 T (in ferromagnetic component of SMC) are shown in Fig. 7 for samples only differing in magnetic particle sizes while technological manufacturing process, resin content and used materials were identical. The decrease of WDC with the increasing particle size was observed for Bm starting from 0.2 T up to the maximum measured value 1.0 T (Fig. 7) which can be related to the predominance of Barkhausen jumps in this range of induction Bm. Furthermore, in case of smaller particle sizes the higher amount of particles stands also for more pinning sites hindering the domain wall movement (defects as well as particle surfaces) [13,21,22]. Values of WDC for Bm of 0.1 T show even a slight increase with the increasing particle sizes – Fig. 7. At very low inductions Bm the reversible domain wall displacements play a dominant role and we assume that in this case, conversely, the higher number of particles in sample is of advantage, as more movable domain walls can be present than in the composite with larger particles but a lower number of particles.
Table 1 Magnetic induction Blmax where total permeability reaches maximum (values for each resin content are approximately identical within the measurement error of 0.01 T). Sample
F45-5%
F75-5%
F100-5%
F160-5%
F45-10%
F75-10%
F100-10%
F160-10%
F45-15%
F75-15%
F100-15%
F160-15%
Blmax (T)
0.37
0.37
0.38
0.37
0.27
0.28
0.27
0.28
0.23
0.22
0.23
0.23
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Fig. 5. Determination of low and high induction losses on hysteresis loop.
4. Thermal and electrical properties Since the magnetic components in electromagnetic devices are usually being heated during their operation in AC magnetic fields, it is considered to be of importance to investigate also the thermal properties of magnetic materials, particularly the heat outflow to prevent the component overheating. It is especially needed when a composite material cannot be operated under higher temperatures e.g. when it contains an organic binder. One of the key quantities characterizing thermal behaviour of materials is the thermal diffusivity a, which describes the heat flowing rate through a material – the ability to conduct the thermal energy relative to the ability to store it [23,24]. A few models exist for thermal diffusivity of heterogeneous materials, e.g. the Parallel model, the Agari-Uno model, the symmetric and asymmetric Bruggeman model or the Cheng-Vachon model [15,24], some of them not originally developed for the thermal diffusivity calculation, but applying mathematical analogy to various transport coefficients. One of such mathematical models holding for e.g. electric conductivity, heat conductivity, thermal diffusivity, electric permittivity or magnetic permeability of a composite material is the model by Hashin and Shtrikman [15,25], originally developed for magnetic permeability of a homogeneous multi-phase system. In general the thermal diffusivity a of a homogeneous body is defined as the thermal conductivity k divided by the density q and the specific heat capacity cP at a constant pressure [23,24] (unit mm2 s1):
a¼
k
qc P
ð6Þ
:
According to the Hashin and Shtrikman model the thermal diffusivity a of SMC composed of a resin matrix with thermal diffusivity aR and a volume fraction of iron particles x with thermal diffusivity aFe is calculated first as the case when iron particles are perfectly insulated by the resin, this is represented by the Hashin–Shtrikman lower boundary HS
a ¼ aHS ¼ aR
2aR þ aFe 2xðaR aFe Þ : 2aR þ aFe þ xðaR aFe Þ
ð7Þ
As the opposite theoretical case one can assume the iron particles are no longer insulated and the iron becomes the matrix surrounding the resin parts. Then a equals to the Hashin–Shtrikman upper boundary HS+
a ¼ aHSþ ¼ aFe
2aFe þ aR 2ð1 xÞðaFe aR Þ : 2aFe þ aR þ ð1 xÞðaFe aR Þ
ð8Þ Fig. 6. High and low induction losses vs. maximum magnetic induction.
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Fig. 7. DC energy losses of samples with 10 vol.% of resin at Bm from 0.1 T to 1.0 T (in ferromagnetic material).
Real SMC can be usually found between HS and HS+, depending on the quality of insulation of magnetic particles from each other. Schilling and Partzsch [26] calculated the interconnectivity Xic from aHS, aHS+ and experimental value aexp, determining the extent to which iron particles form an ideally interconnected network. The closer the measured value aexp is to the theoretical case of insulated particles aHS, the lower is the value of Xic (for perfectly insulated particles Xic ? 0) [15,24]:
aexp aHS X ic ¼ HSþ : a aHS
Fig. 8. Thermal diffusivity as a function of temperature.
ð9Þ
In Fig. 8 the measured dependence of thermal diffusivity on temperature in the range from 40 to 200 °C is shown, a decreases with the increasing resin content, as expected, but no dependence on magnetic particle size was observed (also found in [15]). The decrease of a with temperature is due to the increase of the velocity v and free path length l of phonons, a = 1/(3vl). From Eqs. (7), (8) lower and upper boundary HS and HS+ were calculated (aFe 23 mm2 s1, aR 0.1 mm2 s1 – literature values for t 25 °C [27], and the porosity was taken into account with a of an air at high compacting pressure to be even lower than aR [28]), in Table 2 values of aHS and aHS+ are shown for samples with 5 vol.%, 10 vol.% and 15 vol.% of resin. We see that the measured values of a for all samples are much closer to lower boundary HS than to upper boundary HS+, revealing that iron particles are relatively well insulated from each other. This fact is also confirmed by low values of Xic (calculated from Eq. (9)). In Table 2 the ranges of minimum to maximum values for each volume fraction of the resin are shown. In the view of practical application of soft magnetic composite material, in which thanks to the particle insulation much lower values of energy losses can be reached causing lower heating of the composite, the much lower thermal diffusivity compared to bulk iron material is then sufficient for the lower heat outflow rate. The measured specific electrical resistivity qR as a function of mean magnetic particle size is plotted in Fig. 9. It was observed that qR decreases with the increasing magnetic particle size: for samples with 15 vol.% of resin it was from 360 mX m down to 1.4 mX m, for samples with 10 vol.% of resin from 16 mX m down to 0.8 mX m and for samples with 5 vol.% of resin from 2.2 mX m down to 0.18 mX m. Values of qR of all samples are relative high compared to similar composites investigated e.g. in [29–31], revealing good insulation of particles. Both the thermal diffusivity and the specific resistivity measurements indicate that the iron particles in composite samples
Table 2 Hashin–Shtrikman lower and upper boundaries and the interconnectivity of the samples. Samples (resin content) (vol.%)
Hashin–Shtrikman lower boundary HS (mm2 s1)
Hashin–Shtrikman upper boundary HS+ (mm2 s1)
Interconnectivity (–) (min.–max. value)
5 10 15
1.56 0.96 0.77
17.92 15.38 14.05
0.002–0.021 0.015–0.04 0.002–0.015
Fig. 9. Specific resistivity as a function of mean magnetic particle size.
are quite well insulated. The quality of insulation of magnetic particles has a direct connection with the magnetic interaction between the particles through the inner demagnetizing fields – observed and explained in [13]: The more the magnetic particles
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are insulated from each other, the higher are the demagnetizing fields causing lower interaction between the particles and resulting in lower number of movable domain walls leading to less irreversible magnetization processes overall [13]. 5. Summary and conclusions In this work the proportions of reversible and irreversible magnetization processes in iron–phenolphormaldehyde resin composite samples differing in magnetic particle size and resin content were studied in the frame of magnetic, thermal and electrical properties. The investigation was focused on the magnetic permeability, the DC energy losses, the specific resistivity as well as the thermal diffusivity. The following results were obtained: 1. At very low inductions B ? 0 T the magnetization process is 100% reversible. Depending on resin content the induction at maximum permeability Blmax (limiting induction) varies from 0.22 T to 0.38 T. At the limiting induction Blmax the magnetization process is 50–65% reversible depending on resin content. Exceeding Blmax the rotation of magnetization vector becomes more and more important and magnetization processes are reversible up to 60–80% at B = 0.8 T. Proportion of irreversible processes is decreasing with resin content and also with reduction of magnetic particle size. This can be explained by demagnetizing fields at particle surfaces leading to a decrease of number of movable domain walls, as in case of larger particles and lower resin content the higher number of movable domain walls more likely overcome pinning centres, meaning more Barkhausen jumps. These observations were verified by permeability measurements as well as by separation of losses into low and high induction losses. 2. The thermal diffusivity was found to be decreasing with the increasing resin content, but no dependence on magnetic particle size was observed (contrary to the specific resistivity, which was decreasing with increasing particle size). The comparison with Hashin–Shtrikman model indicated a good insulation of iron particles from each other, resulting in low interaction between particles and therefore a low number of movable domain walls overall.
Acknowledgements This work was realized within the frame of the projects ‘‘Centre of excellence of progressive materials with nano and submicrostructure’’ ITMS 26220120019 and ‘‘Research centre of progressive materials and technologies for present and future applications’’ ITMS 26220220186 PROMATECH, supported by the Operational Program ‘‘Research and Development’’ financed through European Regional Development Fund. This work was also supported by the Slovak Research and Development Agency under the Contract No. APVV-0222-10 MAGCOMP and by the Scientific Grant Agency of the Ministry of Education of Slovak Republic and the Slovak Academy of Sciences, project VEGA No. 1/0861/12. References [1] K.H.J. Buschow, Concise Encyclopedia of Magnetic and Superconducting Materials, Elsevier, Oxford, UK, 2005. [2] S. Giménez, T. Lauwagie, G. Roebben, W. Heylen, O. Van der Biest, Effects of microstructural heterogeneity on the mechanical properties of pressed soft magnetic composite bodies, J. Alloys Comp. 419 (2006) 299–305.
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